A Combinatorial Formula for Orthogonal Idempotents in the $0$-Hecke Algebra of the Symmetric Group

Details A Combinatorial Formula for Orthogonal Idempotents in the $0$-Hecke Algebra of the Symmetric Group A Combinatorial Formula for Orthogonal Idempotents in the $0$-Hecke Algebra of the Symmetric Group

2010-08-13

arxiv.org/abs/1008.2401v1

Mathematics

Representation Theory

25 pages, 2 figures

Scientific paper

Building on the work of P.N. Norton, we give combinatorial formulae for two
maximal decompositions of the identity into orthogonal idempotents in the
$0$-Hecke algebra of the symmetric group, $\mathbb{C}H_0(S_N)$. This
construction is compatible with the branching from $S_{N-1}$ to $S_{N}$.

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